This picture of the classical dynamics remains being a conjecture, although it is widely accepted and numerous numerical studies confirm the described behavior [1]}, [2]}, [3]}.
But let us remark that the BKL scenario takes place very close to the singularity.
Therefore, at this stage, one would
expect quantum effects to become relevant in the analysis. However, it is still unclear how this scenario can be modified when
quantum effects are taken into account. In the literature, there are several approaches to quantum models of Bianchi IX, focused on different features and questions (as the avoidance of the singularity or the survival of the chaotic behavior) [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, as well as simpler approaches to Bianchi II quantum models [16]}, [17]}, [18]}, [19]}.
